I have a wooden sculpture of a bear that I would like copied into
bronze. (Search on the words "bear" + "ainu" in eBay to see the size
and complexity of the type of sculpture I'm referring to.)

What is the best way to do this? By best I mean easiest and cheapest.
I would also consider having it copied into a fake stone material as
well if it was much cheaper. Please provide information on both
options. (If you know of a third option, by all means, let me know.)

Who would I go to? How much would they charge? Is it possible for an
amateur to do it at home?

I tip upwards of 50 to 100% for particularly thorough responses.

Thanks in advance for your help.

Here are two sites that allow you to have an object cast in bronze :

http://www.paradagallery.com/castbronze.htm
http://www.ruidoso.net/crucis/

To get a price, you would have to get in contact with them.

This site provides various other sorts of materials to be cast in,
including something that resembles bronze, or even plaster, probably
with a lower price than a pure bronze sculpture:

http://www.djstudios.net/

Hope this helps.